Electricity

Vibration-to-Electric Energy Conversion Using aMechanically-Varied Capacitor

by

Bernard Chih-Hsun Yen

Bachelor of Science in Electrical Engineering and Computer ScienceUniversity of California at Berkeley, 2003

Submitted to the Department of Electrical Engineering and Computer Sciencein partial fulfillment of the requirements for the degree of

Master of Science

at the

MASSACHUSETTS INSTITUTE OF TECHNOLOGY

February 2005

@ Bernard Chih-Hsun Yen, 2005. All rights reserved.

The author hereby grants to MIT permission to reproduce and distribute publiclypaper and electronic copies of this thesis document in whole or in part.

Author.......

C i d b

... .. .. ... ...... .....

Department of Electrical Engineering and Computer ScienceJanuary 14, 2005

..y.Jeffrey H. Lang

Associate Director, Laboratory for Electronic and Electromagnetic SystemsThesis Supervisor

Accepted by ....

Chairman, Departmental Committee on

!MSACHUSETS INSTITUTE.OF TECHNOLOGY

MAR 14 2005

LIBRARIES

Arthur C. SmithGraduate Students

AACHIVES

t U e:

Vibration-to-Electric Energy Conversion Using aMechanically-Varied Capacitor

byBernard Chih-Hsun Yen

Submitted to the Department of Electrical Engineering and Computer Scienceon January 14, 2005, in partial fulfillment of the

requirements for the degree ofMaster of Science

Abstract

Past research in vibration energy harvesting has focused on the use of variable capac-itors, magnets, or piezoelectric materials as the basis of energy transduction. How-ever, few of these studies have explored the detailed circuits required to make theenergy harvesting work. In contrast, this thesis develops and demonstrates a cir-cuit to support variable-capacitor-based energy harvesting. The circuit combines adiode-based charge pump with an asynchronous inductive flyback mechanism to re-turn the pumped energy to a central reservoir. A cantilever beam variable capacitorwith 650 pF DC capacitance and 347.77 pF zero-to-peak AC capacitance, formed bya 43.56 cm 2 spring steel top plate attached to an aluminum base, drives the experi-mental charge pump near 1.56 kHz.

HSPICE simulation confirms that given a maximum to minimum capacitance ratiolarger than 1.65 and realistic models for the transistor and diodes, the circuit canharvest approximately 1 ptW of power. This power level is achieved after optimizingthe flyback path to run at approximately 1/4 of the mechanical vibration frequencywith a duty ratio of 0.0019. Simulation also shows that unless a source-referencedclock drives the MOSFET, spurious energy injection can occur, which would inflatethe circuit's conversion efficiency if the harvester is driven by an external clock.

A working vibration energy harvester comprising a time varying capacitor with acapacitance ratio of 3.27 converted sufficient energy to sustain 6 V across a 20 MQload. This translates to an average power of 1.8 pW. Based on a theoretical harvestinglimit of 40.67 pW, the prototype achieved a conversion efficiency of 4.43 %. Additionalexperiments confirm that the harvester was not sustained by clock energy injection.Finally, the harvester could start up from a reservoir voltage of 89 mV, suggestingthat the circuit can be initiated by an attached piezoelectric film.

Thesis Supervisor: Jeffrey H. LangTitle: Associate Director, Laboratory for Electronic and Electromagnetic Systems

3

Acknowledgments

I owe a huge intellectual debt to numerous individuals working at the Laboratory

for Electronic and Electromagnetic Systems for their help during the development

of this thesis. Professor Dave Perreault provided excellent suggestions on the diode

selection as well as alternative energy flyback techniques. The vacuum chamber for

the variable capacitor and the surface mount PCB used in the final stage of testing

were produced at lightning speed by Wayne Ryan, whose knowledge on prototyping is

truly amazing. Jos6 Oscar Mur-Miranda, Joshua Phinney, Lodewyk Steyn, Matthew

Mishrikey, and Yihui Qiu helped me ease the transition into LEES early on and

provided unwavering support whenever I ran into difficulties. Professor Thomas Keim

secured my internship at Engineering Matters, Inc., which allowed me to continue

researching during the summer.

The redesign of the variable capacitor occurred with plenty of guidance from

both Professor Alex Slocum, Alexis Weber, and Gerry Wentworth. Alexis stayed

overtime on numerous occasions to help me run the Pro/Engineer Wildfire finite

element analysis in order to optimize and correct the out-of-plane resonant frequency.

Gerry provided much help during the final prototyping on the waterjet and made theprocess as painless as it could be.

Schmidt Group Laboratory provided the necessary equipment to excite the pro-

totype variable capacitor, which was crucial to the collection of experimental data.

In particular, I want to thank Professor Martin Schmidt and Antimony Gerhardt for

coordinating the effort that allowed the shaker table and amplifier to remain checked

out for extended amounts of time. Your generosity will not be forgotten.

I also want to extend a warm thank you to Professor Charles Sodini for spending

time to work out the clock power injection issue in the energy harvesting circuit.

5

Without the insight of using a source-referenced gate drive, the research would not

have been able to move past the simulation stage. Someday, when I find a coin worthy

of this knowledge, it will be promptly deposited into your money jar.

My parents, Gili and Eva Yen, provided much guidance and moral support during

my educational career and allowed me to reach where I am today. Their care and

understanding go way beyond the norm, and I am forever grateful. This thesis belongs

to them as much as it does to me.

Professor Jeffrey Lang deserves my deepest gratitude, not only as my thesis ad-

viser but as someone who truly cares about me in every possible way. He offered

me a research position at a time when I felt extremely stressed because no other

opportunities existed. Throughout this research, he provided countless suggestions

for overcoming difficult theoretical and experimental barriers. Without these critical

insights, this thesis would not exist. I will never forget all the time he spent with

me both during and after research meetings, even when he already had many other

businesses to attend to. Furthermore, he never hesitated to remind me to rest when

I had exams in the courses I was taking, or when my teaching assistant load grew too

high. Thank you! I cannot possibly repay all this kindness and care.

6

Contents

14

. . . . 15

. . . . 17

. . . . 18

. . . . 21

1 Introduction

1.1 Concept of Energy Harvesting . . . . . . . .

1.2 Reasons to Research . . . . . . . . . . . . .

1.3 Previous Works . . . . . . . . . . . . . . . .

1.4 Chapter Summary . . . . . . . . . . . . . .

2 Foundations of Energy Harvesting

2.1 The Q-V plane . . . . . . . . . . . . . . . .

2.2 A Synchronous Charge-Constrained Circuit .

2.3 The Asynchronous Topology: An Overview .

2.4 Limitations Without Flyback . . . . . . . .

2.5 Energy Flyback Technique . . . . . . . . . .

2.6 Bucket Brigade Capacitive Flyback . . . . .

2.7 Relevant Measuring Techniques . . . . . . .

2.8 Chapter Summary . . . . . . . . . . . . . .

23

. . 24

26

. . 28

29

36

. . 39

. . 44

46

3 Circuit Simulation and Design

3.1 Creating the Variable Capacitor . . . . . . . . . . . . . . . . . . . . .

3.2 Inductor Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.3 Power Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7

48

48

50

51

3.4 Oscilloscope Probes . . . . . . . . . . . .

3.5 Gate Drive Modeling . . . . . . . . . . .

3.6 Simulating the Two Diode Circuit . . . .

3.7 Two Diode Circuit with Energy Flyback

3.8 Gate Drive, A First Attempt . . . . . . .

3.9 Corrected Gate Drive . . . . . . . . . . .

3.10 Parameter Optimization . . . . . . . . .

3.10.1 Effect of Inductor Parasitics . . .

3.10.2 Effect of Clock's Duty Ratio . . .

3.10.3 Effect of Capacitance Variation .

3.10.4 Effect of Capacitor Values . . . .

3.10.5 Effect of Initial Voltage Level . .

3.10.6 Effect of Diode Leakage . . . . .

3.10.7 Effect of Rise and Fall Time . . .

3.11 Chapter Summary . . . . . . . . . . . .

4 Experimental Results

4.1 Aluminum Block Capacitor Characterization . . . . .

4.2 Energy Harvesting with Aluminum Capacitor . . . .

4.3 Design of a Cantilever Beam Capacitor . . . . . . . .

4.3.1 Qualitative Description . . . . . . . . . . . . .

4.3.2 Setting the Effective Spring Constant . . . . .

4.3.3 Dimensioning the Cantilever Beams . . . . . .

4.3.4 Gap Engineering . . . . . . . . . . . . . . . .

4.3.5 Calculating the Capacitance Variation . . . .

4.3.6 Second-Order Spring Constant Consideration

8

. . . . . . . . . . . . . . . . 5 2

. . . . . . . . . . . . . . . . 5 3

. . . . . . . . . . . . . . . . 5 3

. . . . . . . . . . . . . . . . 5 7

. . . . . . . . . . . . . . . . 6 1

. . . . . . . . . . . . . . . . 6 6

. . . . . . . . . . . . . . . . 6 8

. . . . . . . . . . . . . . . . 6 9

. . . . . . . . . . . . . . . . 7 0

. . . . . . . . . . . . . . . . 7 1

. . . . . . . . . . . . . . . . 7 2

. . . . . . . . . . . . . . . . 73

. . . . . . . . . . . . . . . . 7 4

. . . . . . . . . . . . . . . . 7 5

. . . . . . . . . . . . . . . . 7 5

77

. . . . . . . 78

. . . . . . . 82

. . . . . . . 85

. . . . . . . 86

. . . . . . . 87

. . . . . . . 88

. . . . . . . 89

. . . . . . . 89

. . . . . . . 92

4.4

4.5

4.6

4.7

4.8

4.9

4.10

4.11

4.3.7 Design Verification Using FEM . . . .

4.3.8 Additional Design Considerations . . .

Characterizing the Cantilever Beam Capacitor

Energy Harvesting with Steel Capacitor . . . .

Starting Up the System . . . . . . . . . . . .

Sensitivity to Frequency Variation . . . . . . .

Simulation Revisited . . . . . . . . . . . . . .

Energy Conversion Verification . . . . . . . .

Energy Conversion Efficiency . . . . . . . . .

Chapter Summary . . . . . . . . . . . . . . .

5 Summary, Conclusions, and

5.1 Chapter Summaries . . . .

5.2 Important Conclusions . .

5.3 Future Improvements . . .

5.4 Interfacing with the Load

5.5 Final Words . . . . . . . .

. . . . 95

. . . . 97

. . . . 98

. . . . 100

. . . . 104

. . . . 105

. . . . 106

. . . . 110

. . . . 115

. . . . 119

Possible Future Work 120

. . . . . . . . . . . . . . . . . . . . . . . . 120

. . . . . . . . . . . . . . . . . . . . . . . . 123

. . . . . . . . . . . . . . . . . . . . . . . . 124

. . . . . . . . . . . . . . . . . . . . . . . . 126

A HSPICE Simulation Code

A.1 Complete Simulation Deck . . . . . . . . . . . . . . . . . . . . . . .

A.2 Device Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

127

128

128

130

9

List of Figures

2-1 Two typical electric energy conversion cycles . . . . . . . . . . . . . . 25

2-2 Charge-constrained energy harvesting circuit using two MOSFETs. . 26

2-3 Block diagram of capacitive energy harvester. . . . . . . . . . . . . . 28

2-4 Charge-pump portion of energy harvesting circuit. . . . . . . . . . . . 29

2-5 Equivalent circuit diagram of one idealized energy harvesting cycle. 30

2-6 Charge-constraining portion of non-ideal energy harvesting circuit. 33

2-7 Equivalent circuit diagram of one non-ideal energy harvesting cycle. 34

2-8 Idealized inductive energy flyback circuit diagram. . . . . . . . . . . . 37

2-9 Idealized capacitive energy flyback circuit diagram. . . . . . . . . . . 38

2-10 A possible bucket brigade energy flyback circuit. . . . . . . . . . . . . 40

2-11 Flyback efficiency versus number of bucket brigade capacitors. ..... 43

2-12 Op-amp based network to extract capacitance variation magnitudes. 44

2-13 Circuit to accurately determine the DC value of a capacitor. . . . . . 45

3-1 Subcircuit for simulating a variable capacitor. . . . . . . . . . . . . . 49

3-2 Two-port input current of variable capacitor. . . . . . . . . . . . . . . 50

3-3 Inductor modeled with core loss and winding loss. . . . . . . . . . . . 51

3-4 Charge pump portion of the energy harvester. . . . . . . . . . . . . . 54

3-5 Voltage waveforms for energy harvesting circuit. . . . . . . . . . . . . 54

3-6 Current waveforms for charge pump circuit. . . . . . . . . . . . . . . 56

10

3-7 The complete energy harvesting circuit without gate drive. . . . . . . 58

3-8 VRES as a function of time for an ideally driven circuit. . . . . . . . . 59

3-9 VVAR and vs as a function of time for an ideally driven circuit. .... 60

3-10 iD1 and iD2 as a function of time for an ideally driven circuit. . . . . . 61

3-11 VRES as a function of time for a ground-referenced CLK drive. .... 63

3-12 Cycle of circuit operation that results in energy injection from CLK. . 65

3-13 Energy harvesting circuit with source-referenced flyback clocking. . . 66

3-14 vs as a function of time for slow energy flyback clocking. . . . . . . . 68

3-15 vs as a function of time for Cs = 10 nF. . . . . . . . . . . . . . . . . 73

4-1 Energy harvesting PCB attached to an auxiliary breadboard. . . . . . 78

4-2 Side-view of the aluminum block capacitor (not to scale). . . . . . . . 79

4-3 Ling Dynamic System V456 shaker table. . . . . . . . . . . . . . . . . 80

4-4 VOUT as a function of shaking strengths. . . . . . . . . . . . . . . . . 82

4-5 CAC as a function of shaking strength. . . . . . . . . . . . . . . . . . 83

4-6 Frequency sweep used to determine variation in quality factor. ..... 84

4-7 Waveform of vs for aluminum capacitor with VAMP,p-p = 100 mV . 85

4-8 HSPICE waveform of vs for CDC = 752.4 pF and CAC = 10.33 pF . 86

4-9 Waveform of VRES for aluminum capacitor with different shaking. . 87

4-10 Equivalent mechanical model of the top capacitor plate. . . . . . . . . 90

4-11 Cantilever beam when the proof mass is at maximum vertical travel. . 93

4-12 Pro/Engineer Wildfire finite element analysis results. . . . . . . . . . 95

4-13 Final design for the new variable capacitor, completely assembled. . . 97

4-14 Frequency sweep for the spring steel variable capacitor. . . . . . . . . 99

4-15 CAC as a function of shaking strength. . . . . . . . . . . . . . . . . . 100

4-16 Amplifier VOUT as a function of shaking strengths. . . . . . . . . . . . 101

11

4-17

4-18

4-19

4-20

4-21

4-22

4-23

4-24

4-25

4-26

4-27

4-28

4-29

4-30

4-31

4-32

4-33

12

Baseline experiment to gauge first order decay at VRES . . . . . . . . 102

First order decay at VRES for increasingly heavy shaking. . . . . . . . 103

Plot of VRES as VAMP,p-p changes from 250 mV to 380 mV. . . . . . . 104

Rising curves at VRES for increasingly heavy shaking. . . . . . . . . . 105

Plot of VRES as circuit starts up from VINIT = 200 mV. . . . . . . . . . 106

Plot of VRES as a function of frequency with VAMP,p-p= 320 mV. . . . 107

LC network used to characterize the nonlinear inductor core loss. . . 108

Plot of and #c as a function of VDR,p-p at f = 865 Hz . . . . . . 108LC network used to model the nonlinear core loss in HSPICE. ... . 109

Comparison of the piecewise linear functions modeling Rc. . . . . . . 110

VRES as a function of time with nonlinear core loss. . . . . . . . . . . 111

VRES as a function of time with nonlinear core loss. . . . . . . . . . . 112

VRES as a function of reservoir loading with VAMP,p-p = 0 mV..... 113

VRES as a function of reservoir loading with VAMP,p--p = 100 mV. . 114

VOUT for both top and bottom plate grounding strategy . . . . . . . . 115

VRES as a function of clocking voltage . . . . . . . . . . . . . . . . . . 116

Q-V plane trace representing theoretical harvesting maximum. . . . . 117

List of Tables

Ideal converted power as a function of fCLK - - - -

Converted power as a function of VG . . . . . . .

Converted power as a function of fCLK . . . . . . .

Converted power as a function of vGS . . . . . . . .

Converted power as a function of fCLK . . . . . . .

Converted power as a function of RC and Rw. . ,

Converted power as a function of D . . . . . . .

Converted power as a function of CAC. . . . . .

Converted power as a function of CRES and Cs.

Converted power as a function of VINIT . . . . . .

Converted power as a function of Is . . . . . . .

Converted power as a function of tRISE and tFALL-

4.1 CAC of aluminum block capacitor as a function of shaking strength. .

13

3.1

3.2

3.3

3.4

3.5

3.6

3.7

3.8

3.9

3.10

3.11

3.12

- . . - . . . . 62

- . . - - . .. 64

- . - . . - .. 64

- . - . . ... 67

- . .. . ... 67

. . . . . . . . 69

. . . . . . . . 70

- . .. - ... 71

. . . . . . . . 72

- - - - - . - - 74

- . . . . . . . 74

- . . .. - . . 75

81

Chapter 1

Introduction

More than two thousand years ago, Greeks and Romans used waterwheels, placed

strategically along streams, to mechanically rotate gears that helped grind corn. This

simple idea spread around the world, and over the centuries, people built upon the

original design in hopes of improving the conversion efficiency between flowing water

and useful energy. In 1862, turbines situated in Wisconsin managed to produce

12.5 kW of power based solely on water gushing through the equipment when the

dam doors opened. The above development serves to illustrate that the concept of

energy harvesting is nothing new. Rather, the methodology and principles of creating

an efficient system evolves.

Scavenging the energy of ambient vibrations constitutes one such methodology,

and this will be the focus of the present thesis. Broadly speaking, vibration energy

harvesting involves the creation of some physical structure that can couple in kinetic

energy from small vibrations and convert it into storable electric energy. Due to

the growing demand of autonomous sensors that must function without the need for

human intervention, interest in this topic has burgeoned in recent years. Although

other methods of energy scavenging, such as those involving thermal and chemical

gradients, tidal waves, and photons, are also being actively researched, the wide

availability of vibration energy makes it a very good candidate, and this thesis will

14

show that the parts necessary to carry out such energy harvesting are relatively simple.

This chapter presents a broad overview of the current affairs in vibration energy

harvesting, including the different methods presently employed as well as the reasons

behind the continual interest in this topic. Furthermore, important achievements

documented in the literature will be summarized and categorized.

1.1 Concept of Energy Harvesting

Fundamentally, energy harvesting involves the conversion of ambient energy such as

light, heat, or mechanical motion into electrical energy that can directly power an

external system or be stored in battery cells for future use. If the energy source

is further limited to mechanical kinetic energy, or vibrations, three main strategies

of conversion dominate: piezoelectric, magnetic, and electric. Magnetic conversion

can be further subcategorized into systems with varying inductance and systems

that employ moving permanent magnets. Likewise, electric conversion uses either a

time varying capacitor or a permanent electret, where a fixed charge distribution is

introduced in the dielectric layer between the capacitor plates. Although the scope of

this thesis covers variable capacitor electric energy harvesting only, all three strategies

have their own merits.

Piezoelectric materials, such as quartz and barium titanate, contain permanently-

polarized structures that produce an electric field when the materials deform as a

result of an imposed mechanical force [1]. Such a mechanically excited element canbe modeled as a sinusoidal current source with a capacitive source impedance [2] wherethe amplitude of the current depends on the amount of force applied. Therefore, if

this structure is placed near a constantly vibrating source, such as office walls near a

construction site, it can harvest the vibration energy and generate electric power.

Magnetic energy harvesting, on the other hand, seeks to convert vibrational kinetic

energy into an induced voltage across coils of wire, which then can deliver power to an

15

appropriate load. This is typically done by attaching either a permanent magnet, such

as that made from Neodymium Iron Boron, or a coil of wire onto a cantilever beam

that is vibrationally actuated [3]; the other one remains fixed. In either scenario,the coil will cut through magnetic flux as the cantilever beam vibrates, creating an

induced voltage in accordance to Faraday's law. Vibration energy can also be coupled

into the system through the use of a variable inductor, although no studies have been

done on this to date due to inherent advantages of using permanent magnets. While

this method of energy harvesting possess very high conversion efficiency, magnets,

bulky in nature, make these type of systems difficult to integrate with the load it is

driving.

Finally, electric energy harvesting couples vibration energy into the system by

having it perform work on charges via the electric field between parallel plate capac-

itors. In a typical scenario, charges are injected onto capacitor plates when they areclosest together, meaning that the capacitance is at its maximum. Because charges

of opposite polarity reside on the separate plates, the plates tend to collapse when no

external force is applied. Therefore, as vibration energy separates the two plates, it

performs positive work on the charges, which are then drained from the plates when

the capacitor voltage is highest and harvested using power electronics. Besides the

variable capacitor, one can also employ a layer of embedded charge, or electret, in the

dielectric to carry out electric energy harvesting [4]. Such a distribution of permanentcharges induces a voltage on the capacitor plates, polarizing them. As external vi-

bration moves the capacitor plates and alters the capacitance, charge transport along

the plates delivers power to the load. Most state of the art electret systems currently

have power densities inferior to those found in variable capacitor systems, so the vari-

able capacitor is preferred until further advances are made in the use of embedded

charges.

16

1.2 Reasons to Research

Although the method of harvesting energy varies vastly, the ultimate goal of all vi-

bration energy harvesters is to deliver the converted electrical energy to an attached

load that requires power. One might question the necessity of expunging proven

techniques of expending electrochemical energy stored on batteries in favor of energy

harvesting circuits, some of which cannot perform nearly as efficiently compared to

batteries. In reality, while batteries can painlessly power common household items

including alarm clocks, radios, and wireless keyboards, many scenarios require ex-

tended lifetime a typical battery cannot provide. Batteries are also limited to certain

temperature ranges; beyond those ranges, they begin to malfunction.

Consider the difficulty of powering an RF sensor network that must operate in

harsh environments for prolonged periods of time, perhaps a couple years. In military

applications, motion sensors used for tracking enemy movement might be dropped

into enemy territories from low-flying planes. Or, seismological sensors could be

deployed in uninhabited areas accessible only by helicopters. As a final example,

wildlife researchers tracking the behavior of rare bird species might need RFID chips

placed on birds; trying to replace the batteries on these radio frequency tags after

releasing the birds back into nature is difficult and time consuming. Even when the

research can be completed within the battery lifetime, poisonous mercury pollution

from battery corrosion can occur if they are not ultimately recovered.

In all these cases, the sensors must be autonomous as far as energy supply goes,

since physical access to the units is costly, if not impossible. Even if battery replace-

ment were possible, trying to switch out batteries from thousands of sensor units

simultaneously require a tremendous amount of manpower, which can be just as, ifnot more, infeasible. With an energy harvesting circuit powering these sensor units,

the above problems can be solved.

Applications of energy harvesting are not limited to sensor networks. In the

17

army, for example, standard issue equipment such as night vision goggles and radio

transmitters require power supplies. However, carrying excess batteries increases the

load on the soldiers, so it is preferable that the electronics be powered off available

ambient energy sources. This might include recoil energy from a rifle or parasitic

compression energy from the sole of a soldier's boot striking the ground [5].

Of course, in order to successfully maintain power delivery to its load, an energy

harvesting circuit needs to fulfill two requirements: efficiency and the ability to store

converted energy. Vibrations in nature, although common, usually do not occur at

very high frequencies. Typical frequencies might range from a few hertz to a couple

kilohertz. High conversion efficiency insures that as much energy as possible can

be extracted from these slow vibrations. Furthermore, because there are often dead

times between the occurrence of vibrations, the system must be capable of storing

unused energy efficiently in anticipation of later times when power demand exceeds

the amount harvested.

These two requirements are difficult to meet using traditional energy harvesting

techniques. As a baseline of comparison, solar panels are often only 10-20 % efficient,

whereas the goal of energy harvesting circuits lie around 70-80 % efficiency. Sending

the harvested energy into a capacitive or electrochemical source usually requires the

use of DC/DC converters, a circuit topology falling in the regime of power electronis.

Being able to maintain high efficiency in this energy flyback portion of the system as

the amplitude and frequency of harvested energy change requires careful design.

1.3 Previous Works

A careful literature survey of recent developments in the field of energy harvesting is

appropriate for placing the current thesis in context. However, due to the wide range

of techniques used for energy harvesting, some as unusual as exploiting chemical

and thermal gradients, this thesis will limit the survey to vibrational kinetic energy

18

harvesting only.

Numerous research groups have focused on piezoelectric energy harvesting due to

its potential of achieving the highest converted power per unit volume [6]. Kymissiset al employed unimorph strip made from piezoceramic composite material and a

stave made from a multilayer laminate of PVDF foil inside sport sneakers to harvest

the parasitic kinetic energy generated during walking [5]. An input signal of 1 Hz,similar in frequency to a person walking briskly, produced 20 mW peak power for the

PVDF and 80 mW for the unimorph; this translates to roughly 1-2 mJ per step.

In order to maximize the amount of energy harvested from piezoelectric materials,

Ottman et al developed a DSP-controlled, adaptive DC-DC converter that accurately

determined the duty ratio of the active devices as a function the instantaneous me-

chanical excitation amplitude [7]. They showed that as the mechanical excitationincreases past a certain point, the optimal duty ratio becomes essentially a constant.

A prototype circuit demonstrates a 325 % increase in harvested power using this

technique.

As part of Berkeley Wireless Research Center's (BWRC) goal of making an au-tonomous 1.9 GHz chip-on-board RF transmit beacon, Roundy et al explored the

use of a two layer piezoelectric bender mounted as a cantilever beam that harvested

vibration energy [8]. They showed that with a driving vibration of 2.25 m/s 2 at60 Hz, a maximum of 375pW can be transferred into a purely resistive load. On the

other hand, if a capacitive load is attached to store the harvested energy for later

use, the maximum delivered power drops to 180pW. In this paper, the authors also

implement a shutdown control as part of the power circuitry that prevents the load

from consuming energy stored on the capacitor when the capacitor voltage falls below

a certain threshold.

In the area of magnetic energy harvesting, Williams and Yates derived an equa-

tion relating the amount of generated power as a function of the damping factor

for a generator that consists of a permanent magnet attached to a micromachined

19

spring-mass system [9]. Barring physical limitations of the system, the magnet trav-els a longer distance near resonance due to peaking in the system's transfer function;

this directly translates to increased harvested energy. They note, however, that low

damping factor made the system more frequency selective, so if the ambient vibration

covers a larger frequency spectrum, the resistive load attached to the inductor coil

can be changed to make the harvesting broadband.

Glynne-Jones et al made two actual prototypes of electromagnetic generators used

for powering intelligent sensor systems [3]. In these prototypes, coils were hand woundonto a cantilever beam attached to a shaker table and immersed in magnetic fields

generated from permanent magnets. When mounted on the engine block of a car, the

second prototype device produced an average power of 157 pW and a peak power of

3.9 mW.

Research in capacitive electric energy harvesting focuses on two general areas:

the variable capacitor itself and the power electronic circuitry that processes the

converted energy. Miao et al fabricated and conducted tests on a micro electro-

mechanical system (MEMS) capacitor that can vary its capacitance from 1 pF to100 pF [10]. In a single charge-constrained cycle (refer to Chapter 2), this variablecapacitor is capable of producing 24 pW of power using a 10 Hz vibration. However,they do not show results from actual supporting power electronics circuitry, so the

overall energy harvesting ability of the system is unknown.

Mur-Miranda conducted extensive research, using both a variable capacitor macro

model machined from blocks of aluminum and a MEMS capacitive comb drive trans-

ducer, on an electric energy harvesting circuit topology that exploited the charge-

constrained cycle [11]. Using a bread-board prototype that implemented both thepower electronics and the gate driver control circuitry for the active devices, he

demonstrated energy conversion from the vibrational source and showed that output

waveforms matched theoretical calculations. Due to the inefficiencies of the power

electronics circuit used, however, the converted energy could not be translated back

20

as a gain in voltage at a storage capacitor.

Recently, Miyazaki et al reported a prototype vibration-to-electric variable capac-

itor energy converter that exhibited a measured power generation of 120 nW [12]. The

power electronics used in this experiment resembled that used by Mur-Miranda; two

complementary MOSFET switches regulate the flow of current through an inductor

to charge and discharge the variable capacitor during specific portions of a mechanical

cycle. The measured conversion efficiency of this prototype comes out to 21 %. As

Section 3.8 will show, however, the clock signal driving the MOSFET switches can

inadvertently inject energy into the system, and because measurements relating tosuch injection are not available within this paper, it is unknown what fraction of the"harvested" energy actually came from the vibration source.

From the above literature search, one sees that most fully functional state of

the art energy harvesting systems fall into the piezoelectric and magnetic regimes.

The only working prototype for a capacitive electric energy scavenging system comes

from Miyazaki et al as described in the preceding paragraph, but because possible

clock injection issues did not receive attention there, a more thorough investigationis warranted. This reason, added to the fact that piezoelectric film can harm the

environment and magnetic systems are relatively bulky, paves way for further research

into the capacitive electric energy harvesting scheme.

1.4 Chapter Summary

This chapter served both as an introduction to the world of energy harvesting as well

as motivation for the rest of this thesis. As noted, numerous techniques exist for har-

vesting energy from the environment that otherwise would have been lost. Potential

energy sources include solar power, thermal and chemical gradients, acoustic noise,

and vibration. Vibrational energy harvesting can be furthered divided into piezoelec-

tric, magnetic, and electric, depending on how vibration energy is coupled into the

21

system. All are active areas of research, but this thesis will focus on the variable

capacitor electric conversion process. Emphasis will be placed on the electronics and

circuit topologies as opposed to the implementation of the variable capacitor using

MEMS.

Chapter 2 provides the reader with a review of capacitive electric energy harvest-

ing, sufficient to understand the theoretical, simulation, and experimental results that

follow. Related laboratory measurement techniques will also be discussed. Chapter 3

outlines critical HSPICE simulation results that lead directly to a final design of

the energy harvesting circuit topology, one of the main goals of this thesis. Then,

in Chapter 4, experimental data based on a fabricated circuit board is presented

and compared with computer simulations. Chapter 5 summarizes the thesis and its

conclusions, and presents possible directions for future work in this area of research.

If the reader has access to HSPICE and wishes to modify certain design parameters

and observe the effect they have on conversion efficiency, refer to Appendix (A) forthe complete set of HSPICE decks. The model files of all the active components,which were downloaded off the Internet, are also included.

22

Chapter 2

Foundations of Energy Harvesting

As explained in Chapter 1, there exists a broad array of techniques for energy harvest-

ing, of which piezoelectric, electric, and magnetic are perhaps the most prominent.

Based on the specific harvesting strategy used, electric and magnetic energy scaveng-

ing can be further divided into two subcategories each. Capacitive electric energy

harvesting, the main focus of this thesis, usually relies on either charge-constrained

or voltage-constrained cycles, both of which will be fully explained below. Although

methodologies that fall between these two are also theoretically possible, power elec-

tronics, switch-like in nature, rarely permit them.

In this chapter, the fundamentals behind electric energy harvesting will be ex-

plored. Mathematics relating contours in the Q-V plane to the amount of harvestedenergy per cycle are covered first, followed by a direct application of the formulated

concepts to a charge-constrained circuit topology presented in [11]. An alternativetopology based on self-synchronous diodes, which forms the centerpiece of this the-

sis, is shown next, along with detailed equations that model the charge flow on the

variable capacitor and explain the impact of parasitic diode capacitances. Once the

charge pump portion of the capacitive energy harvester has been developed, an en-

ergy flyback mechanism will be added and analyzed, and the pros and cons for various

flyback techniques will be discussed. The chapter concludes with important labora-

23

tory concepts relevant to the characterization of energy harvesting circuits, including

methods of measuring the AC capacitance of a variable capacitor.

By the end of the chapter, an idealized capacitive energy harvesting circuit with

inductive flyback will have been developed, although decisions on the specific com-

ponent values will be left for Chapter 3. The chosen topology forms the basis upon

which the simulations carried out in the next chapter will be based; further improve-

ments to the circuit will curb the problem of clock energy injection, but the maintopology will not change.

2.1 The Q-V plane

Consider a single capacitor with capacitance C and voltage Vc. At any given time,the energy stored on the capacitor can be expressed as

T? 12 1WC = Coc = -QVC (2.1)2 2

where Q = Cvc from fundamental physics. In a physical system, Q, vc, and C canvary as a function of time. For argument purpose, assume that the distance between

the capacitor plates is variable, implying that C can change. If we plot Q and vcvalues parametrically over time in a Q-V plane as C goes from a maximum value toa minimum value and back up, a graph similar to Fig. 2-1 will result. Note that the

two contours shown in this figure represent typical cases; numerous circuit topologies

produce contours dissimilar to both.

Notice that the slope of lines A and C in both diagram represents the capacitance

value in that duration of the cycle. In drawing these figures, an implicit assumption

is made that the capacitor charging (path A) and discharging (path C) occur muchfaster than the rate at which the capacitance changes. Were this not true, path A

and C would not be straight lines. Finally, note that a "short" path does not imply

24

Enclosed arearepresenting net

converted energyin one cycle.

CMAx B

AC CMIN

V

(a) Charge-constrained

Figure 2-1: Two typical

0

Enclosed arearepresenting net

converted energyin one cycle.

B

CMAX I

AC CMIN

V

(b) Voltage-constrained

electric energy conversion cycles.

that the time duration associated with that path is short; in fact, path B in both

cases takes the longest time to traverse.

The distinction between the two cycle, one charge-constrained and one voltage-

constrained, depends on which variable, Q or V, is held fixed during the time when thecapacitance value drops from maximum to minimum. For circuits where the variable

capacitor is disconnected when the circuit traverses path B, Fig. 2-1(a) shows thatthe charge on the capacitor plates remains fixed as the capacitance decreases. On the

other hand, for circuits that connect the capacitor to a voltage source during path B,

Fig. 2-1(b) illustrates the capacitor voltage remains fixed as the capacitance drops.

Now, consider the area enclosed by path A-B-C in each case. For the charge-

constrained cycle,

(2.2)WCHARGE ~~ QOAVC2where Qo represents the amount of constrained charge on the capacitor plates whenthe plates move apart. For the voltage constrained cycle,

1WVOLTAGE -AQVC,O2 (2-3)

25

a

AL

CVAR 2

L ControlElectronics

CRES ~ ~1

TFigure 2-2: Charge-constrained energy harvesting circuit using two MOSFETs.

where Vc,o represents the constrained voltage when the plates move apart. Comparing

Eq. (2.2) and Eq. (2.3) with Eq. (2.1), it is seen that the enclosed area exactlyrepresents the net energy gained by the capacitor in one cycle [13]. Therefore, theprimary goal of a well designed energy harvesting circuit is to increase the amount

of area surrounded by path A-B-C while retaining high conversion efficiency and the

ability to operate asynchronously.

2.2 A Synchronous Charge-Constrained Circuit

Fig. 2-2 shows an example of a circuit topology that employs the charge-constrained

energy harvesting technique described earlier [11]. Assume that the current throughthe inductor starts at 0 A and that CVAR, initially at its maximum value CMAX, isuncharged. At the beginning of a cycle, M turns on, resulting in iL, the current in

the inductor, ramping up according to VL = LdL. When iL reaches a desired value,M 1 is turned off by the control circuitry and M 2 is simultaneously turned on. Because

of the continuity of iL, CVAR begins to charge up all the while staying at a capacitance

value of CMAx; the mechanical cycle is assumed to be much longer than the electrical

charging and discharging.

Once iL reaches 0 A, the control circuitry turns M 2 off, resulting in CVAR being

isolated from the rest of the circuit. Therefore, as vibrational force causes CVAR to

26

move apart and reach CVAR = CMIN, an energy harvesting cycle is carried out. The

harvested energy can be transferred back to CRES through a reverse cycle of inductor

charging and discharging.

There are several disadvantages to this topology, however. Perhaps the most im-

portant are the need for accurate transistor turn-on and turn-off, power consumption

in the control electronics, and excessive conduction loss. Preliminary simulations in

HSPICE not presented in this work indicate a necessity to hit the turn-on and turn-

off points precisely in order to convert energy efficiently. For example, during the

charging phase of CVAR, M 2 must turn off as soon as iL reaches 0 A, or else it is

possible for resonance between the capacitors and inductor to ring VAR down again.

However, if M 2 turns off too early, parts of the charge extracted from CRES to ramp

up iL will be wasted. There are similar considerations for the second half of the cycle

in which the harvested energy is transferred back to CREs. Such precisions in the gate

drive signals are difficult to achieve due to the delay between the detection of zero

crossing points in iL and the toggling of the MOSFET switches, which can result in

limited conversion efficiency.

Power consumed in driving the MOSFET switches of this topology can be quite

large, due to the complexity of accurately controlling two active devices. In an au-

tonomous sensor IC, this power consumption would directly lower the amount of

stored energy available to drive the energy harvester load. A circuit topology that

requires only one active device is preferred since its gate drive electronics can be

implemented with much less complexity, resulting in decreased power usage.

Finally, there is a severe disadvantage when conduction loss is considered. In

the two transistor topology, current flows through M 1 , M 2 , M 2 , and M 1 respectively,

amounting to 4 transistor conduction losses every scavenging cycle. Given that such

conduction losses are comparable in magnitude to the amount of energy harvested,

this charge-constrained circuit topology is not desirable.

To overcome these flaws, an asynchronous capacitive electric energy harvesting

27

Flyback Circuitry

Load Reservoir Charge Pump -T--ora

Figure 2-3: Block diagram of capacitive energy harvester.

circuit based on diodes, the topology this thesis examines in-depth, will be presented

next. Using uncontrolled devices such as diodes ameliorate stringent clocking require-

ments because they turn on and off synchronously with the movement of the variable

capacitor without the need for current sensors. Therefore, cycle-to-cycle variation will,

in a sense, be automatically tracked. Furthermore, the removal of sensing electronics

decreases the complexity of the overall circuit, resulting in lower power consumption

and hence increased efficiency.

2.3 The Asynchronous Topology: An Overview

Fig. 2-3 illustrates the building blocks of an asynchronous energy harvesting cir-

cuit. The heart of this circuit lies in the charge pump, formed from two diodes and

a variable capacitor, that converts vibration energy into electric energy by moving

charges from reservoir onto the variable capacitor and pushing energized charges into

a temporary energy storage. Both the reservoir and temporary storage consists of a

single capacitor. The flyback mechanism insures that the voltage at the reservoir is

maintained while the load draws power from the reservoir.

First, the charge pump block, connected to the reservoir and temporary storage

capacitors, is examined alone. Consider the circuit shown in Fig. 2-4, which includes

3 capacitors and 2 diodes. In Chapter 3, the precise operation of this circuit will be

explored. For now, an intuitive understanding is developed. Assume that the capaci-

tor starts at its maximum possible value and that all three capacitors are charged to

28

CRES VRES CVAR VVAR CS VS

Figure 2-4: Charge-pump portion of energy harvesting circuit.

voltage vo. Because all the node voltages are equal, diodes D1 and D2 are both off.

Now, through an external means such as vibrational motion, the capacitor plates are

moved apart, causing CVAR to drop. Because the charge on the middle capacitor is

constrained by two diodes that are off, a drop in capacitance implies that VAR must

rise to keep Q = CV satisfied; this corresponds to path B in Fig. 2-1. This rise involtage turns on D 2 , resulting in CVAR partially discharging. Unlike path C, CVAR

does not completely discharge into Cs but stops when VAR VS-. At this point, D 2turns off.

Now, as the capacitor plates move back towards each other, again due to an

external force, the cycle is also charge-constrained because both D1 and D 2 are off. As

CVAR increases, VAR drops, forcing D1 to turn on and resulting in a partial charging

of the variable capacitor. This corresponds roughly to path A. The charging of the

capacitor causes VAR to rise, eventually turning off D1 and returning the circuit to

its starting point. Thus, this circuit acts as a charge pump from CRES to Cs, adding

net stored energy to the capacitor over time.

2.4 Limitations Without Flyback

As more and more energy conversion cycles are carried out, Cs in Fig. 2-4 begins to

accumulate large amounts of charge. Eventually, vs rises so high that the variation

in CVAR is unable to pump more charge to Cs; equivalently, charge can no longer

flow from CRES onto CVAR. The maximum vs given a certain variation in CVAR will

29

D1 D2 D1 D2

VRES CMAX VRES S VSn.1 VRES CMIN Cs T vs

(a) First half of cycle (b) Second half of cycle

Figure 2-5: Equivalent circuit diagram of one idealized energy harvesting cycle.

now be explored using a cycle-to-cycle iteration process. For the first pass of the

derivation, ideal diodes are used, meaning that the forward voltage drop is VD = 0 V,the parasitic diode capacitance is CD = 0 F, and the reverse bias leakage current

coefficient is Is = 0 A.

Assume that the variation limits of CVAR are such that CMIN CVAR CMAx and

that WAR = VRES (i.e. diode D1 has just equalized the voltage between the reservoirand the variable capacitor). Define a complete energy harvesting cycle as the time inwhich CVAR undergoes one capacitance variation from maximum to minimum back to

maximum; take vs,i, where i is an integer index starting at 0, to represent the voltage

on Cs when CVAR = CMAX- Finally, since the variation on CRES is so small, represent

the reservoir capacitor as a constant voltage source.

Fig. 2-5(a) shows the equivalent circuit diagram at the start of cycle n - 1. Atthis point, the total capacitor charge on CvAR and Cs is

Qtotai = CMAXVRES + CSvS,n-1 (2.4)

Now consider the variable of interest in the next cycle, namely vs,n. It is easy to see

that vs does not change once D 2 stops conducting, so analyzing this portion of the

circuit operation when CVAR drops in value and WVAR increases in value is sufficient.

The point where CVAR = CMIN is shown in Fig. 2-5(b).

Because DI does not conduct when WAR > VRES, charge-constrained operation

30

dictates that QT = QVAR + Qs is constant, giving

Cs CMAXVS,n = VsV-1 + VRESCM1N + C sfl CMIN + CS

(2.5)

when CVAR CMIN. Furthermore, initial condition gives Vs,O = VRES.

Define a = --CS and 0 = CM VRES. Eq. (2.5) can then be written asCMIN+CS CMIN+CsS.

VS,n = avs,n-1 + , (2.6)

which is a recurrence relation in variable vs,j. Such a recurrence relation can be solvedby determining the homogeneous and particular solution for the associated recurrence

equation

(2.7)

which is obtained by substituting r' = vs,j into Eq. (2.6). The homogeneous solutionmust satisfy

r" = ar" 1 (2.8)

and therefore by inspection,

s = Kaoz

From Eq. (2.7), one particular solution that works is

VSs = - , (2

which, when combined when the homogeneous solution and simplified, results in

VS,n = Vs(h + Vs =P K CS " +CMIN + Cs

Now, using the initial condition vs,O = VRES,

K = VRES i - CMAXCMIN /

CMAXMVRE

CMIN(2.11)

(2.12)

31

2.9)

.10)

r" = ar"n-1 +0) ,

and so the cycle-to-cycle variation of the storage node voltage is

CMIN CMIN + Cs CMINV, VRS[(i _ CMAX) ( CS ) + ICMAX (213To check that Eq. (2.13) makes sense, substitute the extreme case of n = 0 to

obtain

Vs,O = VRES (2.14)

as expected from the initial condition. To determine the voltage limit on the storage

capacitor without the flyback block illustrated in Fig. 2-3, plug in n = OC to obtain

Us, = URAX - (2.15)CMIN

Eq. (2.15) interestingly indicates that the maximum storage on CS depends on theratio of CMAX to CMIN. Because the efficiency of the energy harvester will inevitably

hinge upon the maximum temporary energy storage capacity, it is reasonable to

explore Eq. (2.15) in more detail. Writing out the terms, the equation becomes

CDC + CAC,- CDC VRES (2.16)

C C AC

where CAC indicates the positive zero-to-peak magnitude of the capacitance variation.

From Eq. (2.16), it is apparent that given a fixed CAC, a smaller CDC will allow vsto reach a higher ultimate value. Hence, minimizing parallel parasitic capacitances

becomes a design goal for this particular circuit topology.

Having worked out the circuit behavior using ideal diodes, now consider the sit-

uation when the diode's junction capacitance Cj is included. The modified circuitdiagram is shown in Fig. 2-6. In order to understand the behavior of this non-ideal

circuit, one cycle needs to be divided up into five stages: D 2 closed, D1 and D2opened, Di closed, D1 and D 2 opened, and D2 closed again. For the equivalent cir-

cuit diagram of each stage, refer to Fig. 2-7. Note that the ordering of the stages is

32

cdl

- vJ,+1CJ2

+ V 2 -D2

~1

CRES VRES CVAR WARTCS- VSI *

Figure 2-6: Charge-constraining portion of non-ideal energy harvesting circuit.

slightly different compared to the ideal case analysis. Here, the cycle begins with D2on instead of D, on. In Stage 1, the amount of charge stored on Cs is

Qs,n-1 = CsVs,n-1 . (2.17)

Now, as the capacitance begins to increase from CMIN, assume, without loss of

generality, that D 2 turns off first before Di turns on; this brings the circuit into

Stage 2. From Stage 1 to Stage 2, the amount of charge at node X is conserved.

Paying attention to the polarity of charge on C32 and Cs carefully, one can write that

Qs - QJ2 = CsVs,n-i . (2.18)

As the capacitor plate moves apart and CVAR - CMAX, D1 turns on and the circuit

enters Stage 3. At this moment, VAR V VRES, so by Kirchhoff's Voltage Law,

VS + VJ2Qs QJ2CS CJ2

VRES

= VRES -

(2.19)(2.20)

Multiplying Eq. (2.18) through by Cs,

QsCs - QJ2Cs = CsVs,n- 1 ,

33

(2.21)

+ + - V1 + + V2 -

VRES CMIN VSn.1 cs VS n-1 VRES s

(a) Stage 1 (b) Stage 2

+ VJ2 +VRES CMAX Cs T VS

(c) Stage 3

CJ1

C 1 CJ2

- Vi+ + VJ2-

VRES T CsT

(d) Stage 4

0- Vi + + +

VRES - CMIN VS,, S VS,n

(e) Stage 5

Figure 2-7: Equivalent circuit diagram of one non-ideal energy harvesting cycle.

which, when substituted into Eq. (2.20), gives

Q sC 2 + QsCs - CsVs,n-i = VRESCSCJ2 - (2.22)

Hence, Qs, the amount of charge on the storage capacitor during Stage 3, is

QS = VRESCSCJ2 + CSVS,n-1 (2.23)CS + CJ2

At the same time, the amount of charge on CVAR is

QVAR = CMAXVRES- (2.24)

Now, again without loss of generality, assume that D1 opens before D 2 turns on,

resulting in charge conservation for both node X and Y in Fig. 2-7(d). This is Stage 4

34

+

Vs

+

Vs

CA1 Ci1

of the circuit operation. Defining QJ2 as the amount of charge on CJ2, the total chargeon all capacitors sums to

QTOT = (Qs - Q2) + (QVAR + Q2) = Qs + QVAR , (2.25)

where Qs and QVAR are defined in Eq. (2.23) and Eq. (2.24).

Finally, D 2 turns on as CVAR drops to its minimum value once more. The charge at

node Z is equivalent to the sum of the charges at node X and Y in Stage 4. Therefore,

by distributing QTOT across the 3 capacitors and solving for vs,,, one obtains that

(Cs + CJ2) (Cn1 + CMIN + CS)CJ1 + CMAX + C S

,n-1 + V+I+CS VRESCJ1 + CMIN + CS

(CS + CJ2) (CR + CMIN + CS)

CJ + CMAX + C2sC3 =CS VRESCn1 + CMIN + CS

(2.27)

(2.28)

Eq. (2.26) can be rewritten as

Vs,n = avs,n-1 + , (2.29)

which is similar to Eq. (2.6) except for the definition of a and 3. The technique forsolving recurrence relation used earlier in the ideal energy harvesting cycle can be

directly applied here. In the end,

(Cn1 +CMIN + CS))(CS + C2) (C 1 + CMAX + C"2C

(Cn1 + CJ2)Cs + (C2 + Cs) CMIN + C0 3 C3 2

(2.30)

(2.31)

35

vsn =

Defining

and

(2.26)

(h)vs,n

(p)vs'n

K((CS + CJ2)

Using the initial condition and defining

(Cs + CJ2) (C + CMAX + CS7 = J2C (2.32)(Cn + CJ2)CS + (CJ2 + Cs) CMIN + C 1C 2 (

the full cycle-to-cycle variation in the storage capacitor voltage is

Vs,n = [(1 - 7) a" + -Y] VRES - (2.33)

Again, check the derived equation with an extreme case of n= 0. Here, Vs,O =

VRES, which is consistent with the initial condition. Since a < 1, substitute n = oo

to yield

VS,o = 7VRES - (2-34)

Grouping terms on the numerator and denominator of Eq. (2.34) makes it apparentthat the voltage limit on the storage capacitor is significantly smaller compared to

the ideal case. Hence, energy harvesting efficiency goes down with increasing Cjl andCJ2, which indicates that diodes with small parasitics are preferred. As Cjl and CJ2approaches 0, vs,, approaches -CA2VRES; this makes sense because diodes without

parasitic junction capacitance are ideal diodes.

2.5 Energy Flyback Technique

So far, the charge pump has been analyzed as a standalone block. However, as seen

from the previous section, the energy harvesting cycle becomes less efficient as charge

builds up on the storage capacitor Cs. Furthermore, referring back to Fig. 2-3, the

load is attached to CRES instead of Cs. In this thesis, the load comprises of a 10 MQscope probe measuring VRES in series with another 10 MQ resistor. Therefore, flyingthe converted energy back into a reservoir capacitor that satisfies CRES > CS mustoccur as part of the circuit operation.

36

LFB

CLK

D1 D2L

Load CRES - VRES CVAR WAR CS -- VS I DFB

Figure 2-8: Idealized inductive energy flyback circuit diagram.

Broadly speaking, there are two main methods of energy flyback: inductive and ca-

pacitive. Inductive flyback, shown in Fig. 2-8 without parasitic components, operates

by first ramping up the current in LFB using a voltage difference across the inductor.

Then, at a later time, the inductive path is disconnected by means of a transistor

switch, forcing current to "freewheel" through DFB in the second half of the flyback

cycle. Topologically, the inductive flyback portion of Fig. 2-8 looks remarkably sim-

ilar to a DC/DC buck converter. The main difference stems from the fact that in

a buck converter, the main objective is to maintain a constant output voltage VOUTwhile the circuit here deliberately tries to pull VRES up as efficiently as possible.

Theoretically, the efficiency of such a flyback system can reach 100 %, but due to

parasitic core and wire loss in the inductor as well as conduction and switching loss in

the MOSFET and diodes, part of the energy is lost. For now, ignore the non-idealities

of the inductor and focus on the conduction loss. Chapter 3 will provide justificationas to why inductor parasitics prove to be non-critical. Assume that the CLK signal is

high enough to force the MOSFET into the triode region. In this case, the conduction

loss is resistive:

(PFET,COND) = KFETVFET) i 0RMSRDS,ON (2.35)

where RDS,ON is the equivalent on-resistance of the MOSFET in triode region. On

the other hand, because a diode exhibits constant forward bias voltage drop across

37

CLK

D , D2L

Load CRES VRES CVAR WAR CS VS

Figure 2-9: Idealized capacitive energy flyback circuit diagram.

its terminals, the conduction loss can be represented as:

(PD,COND) = (iDVD) (iD) VD . (2-36)

In summary, the root-mean-square current is important for a transistor while the av-

erage current is important for a diode. The total energy lost per cycle of an inductive

flyback circuit is therefore

WLossD 1 23 DWRMSDS,ON 7 + (iD) VD (2-fFB fFB

with fFB representing the frequency at which the flyback portion of the energy har-

vesting circuit operates and D representing the duty ratio of the MOSFET.

For a capacitive flyback strategy, such as that shown in Fig. 2-9, the storage and

reservoir capacitor are simply shorted together through a transistor at regular times

during the circuit operation. Energy flyback occurs by way of voltage equalization

between Cs and CRES; given that both D1 and D 2 are off during the time of flyback,charge conservation along with the fact that vs > VRES results in VRES increasing after

the equalization. Mathematically, the total charge initially is

QTOT,O = Csvs + CRESVRES (2.38)

38

and the total initial energy is

~CSVS + 2RE (2.39)WTOT,O = Css + CRESVRES- -9

When the circuit reaches steady state operation after the MOSFET has been turned

on, the voltage on the capacitors equalizes to a final value VF. However, charge is

conserved, leading to

QTOT,F = (CS + CRES) VF = QTOT,O (2.40)1

WTOT,F = -(Cs + CRES)V (2.41)2F

with VF determined from Eq. (2.38) and Eq. (2.40) to be

VF =SS + CRESVRESCs + CRES

Therefore, the amount of energy lost per capacitive flyback cycle is

1 (OsORES 2WLOSS = WTOT,O - WTOT,F ~ CS RES) (VS - VRES) , (2.43)

= 2 CS+ CREs

which increases in magnitude as the voltage difference between the reservoir and

storage node increases. Note that in contrast with the inductive flyback loss, the

capacitive strategy energy loss is independent of the fFB. Despite this independence,

inductive flyback is still superior to capacitive flyback given typical component values.

2.6 Bucket Brigade Capacitive Flyback

The reader might wonder whether using multiple capacitors in the flyback path will

increase the efficiency of energy flyback. An example of such a flyback circuit is shown

in Fig. 2-10. In this diagram, WIN, the energy being fed into the system, comes from

the vibrational source and WOUT, the energy being taken out, goes into the reservoir.

39

WIN S1 2 S23 Sn-2,n-I Sn-1 n WOUT

Vibration C V, C2 V2 . . .. Cn-2 Vn-2 C V-1 V Vn.1 VRES

Figure 2-10: A possible bucket brigade energy flyback circuit.

Imagine C1 as the storage capacitor Cs and the voltage source VRES as the reservoir

capacitor CRES-

In order to calculate the energy flyback efficiency of this setup, the periodic steady

state (PSS) condition must first be determined. PSS denotes the situation in whichall the circuit state variables (i.e. voltages and currents) return to the same valueafter every cycle of circuit operation. In this case, a complete cycle involves the

variable capacitor's capacitance going from maximum to minimum back to maximum,

or equivalently, a single WIN injection.

The exact calculations involved in deriving the PSS condition of an n-capacitor

bucket brigade is extremely involved and offers no additional insight into the circuit

operation. Therefore, a more intuitive approach is offered. First assume all capacitors

are equivalent, meaning that C1 = C2 = ... = Cn-2 = Cn-1 = C. Consider any

capacitor C, 1 < i < n - 1, that is sandwiched between two other neighboring

capacitors. When the switch on its left, Si_,, closes, vi equalizes with vi_ 1 and reaches

some intermediate voltage between the two original values. Then, when the switch

on the right, Si,i+1 , closes, vi equalizes with vi+1 and reaches a different intermediate

voltage. But these two operations are exactly equivalent to averaging the center

voltage with its two neighboring voltage, so one would expect that after many cycles,

the progression of v 1, v2 ,... , Vn- 2 , - becomes linear and evenly spaced.

In fact, that is exactly what happens for a bucket brigade of capacitors in PSS.

40

The PSS voltage on each capacitor can be expressed as

i = V -- (i 1 ) n - 2R E (2.44)

Having determined the PSS condition, the energy flyback efficiency analysis can pro-

ceed. The steps in determining r wherer = T is as follows:WIN

1. Begin with PSS capacitor voltages on the k-th energy flyback cycle of V1(k),

V2(k),- - - , n--2(k), and Vn-1(k)-

2. Inject WIN into the system at C1.

3. One at a time, turn switches S1,2 , S 2 ,3 ,- - -, Sn-2,n-1, and Sn_1, on then off.

Denote this as the switch rippling stage.

4. Determine V1(k+1), V2(k+),- .. , Vn-2(k+1), and Vn-l(k+1) and require that Vi(k+1) -Vi(k) for all i such that 1 < i < n - 1.

During Step 1, the amount of energy stored on C1 is

W,= 1C 2 =24C; (2.45)

all the capacitance values are simply C since they are assumed to be equal, as men-

tioned earlier. After Step 2, the total energy stored on C1 becomes

Q 2W1'0z 2'0, (2.46)Q I20

which, when multiplied through with 2C and simplified, gives

Q1,F = Q ,o + 2CWIN-

Finally, this allows the change in Q, to be calculated:

AQ1 = QI,F - Qi, O Qjo + 2CWIN - Qi0

(2.47)

(2.48)

41

Because all capacitor voltages must return to their original values Vi(k) after Step 3and 4, the entire AQ 1 must ripple all the way through and exit into the voltage sourceVRES. Therefore, WOUT can be determined as

WOUT = AQ1VRES = ( ,o + 2CWIN - Q1,o) VRES - (2.49)The only thing necessary before characterizing 77, the efficiency of a bucket brigade

energy flyback circuit, is the value for Qi,o. This charge can be obtained by examiningthe voltage equalization between C1 and C2 more closely. From Eq. (2.44),

V2,PSS - V1,0 - VES (2.50)n - 2

where vi,pss means the PSS voltage on Ci. Denote the voltage on C1 before Step 2

as vi,0 and the voltage after Step 2 as V1,F. This gives

2-CV1, F = - CVi,0 + WIN (2.51)2 2WIN

V1,F = -, + 2W1N (2.52)

After Step 3 when the switch is closed, the final voltage is the average of V1,F and V2 ,PSSsince the capacitors are equal in value. But this final voltage will be the ultimate

voltage on C1 during this cycle since the switch opens after equalization occurs. In

order to satisfy PSS,

1 1/ Vi0 -VRE5\1V1,F - 1 vl,O - '2 - = v 1,0 . (2.53)

Substituting Eq. (2.52) into Eq. (2.53) and simplifying,

-

2 (n - 1) vRES - 4 (n - 1)2ES -4 (-2n+3) (2.54)-4n + 6

where a = ' (n - 2)2 WIN - VRES. Note that the negative solution for the quadraticequation was selected since vi,o > 0. The required expression for Q1,o is simply

42

0.8 -

0.6 -

eta(n)0.4 -

0.2 -

0.185 0 1 1 10 20 40 60 80 1004 n 100

Figure 2-11: Flyback efficiency versus number of bucket brigade capacitors.

Qi,o = Cvi,o. Finally, referring back to Eq. (2.49), q is

WOUT _ Q, + 2CWIN - Q1,o) VRESWIN WIN

Substituting in the expression for Qi,o into Eq. (2.55) and plotting the result inMathCAD, one obtains an efficiency versus n plot, which is shown in Fig. 2-11. The

efficiency decreases as the number of capacitors increases. Note that because the

derivation is invalid for n < 3, the section of the curve with y > 1 can be safely

ignored.

From the above derivation, it is apparent that the use of a bucket brigade capaci-

tive energy flyback is inferior to the solution of a direct flyback in which Cs is shorted

to CRES through the MOSFET. Another disadvantage of using such a flyback scheme

is the large number of switches involved. Because these switches will be implemented

using discrete transistors, each of them will exhibit conduction loss due to a finite

RON value. Therefore, the actual efficiency will be much smaller than that predicted

by the previous calculation.

43

I I I I0.918 1

C = 100 pF

R = 100 k

VARCVAR +

+

10V V

VOUT

Figure 2-12: Op-amp based network to extract capacitance variation magnitudes.

In summary, the best flyback topology out of the three possible candidates -

inductor, direct shorting switch, and capacitive bucket brigade - is the inductor. Not

only does it possess the highest theoretical flyback efficiency relative to the other two

mechanisms, the inductive flyback is also very simple to implement. The only majordrawback comes from the inherent bulkiness associated with inductors, but because

the design goals do not include minimizing the overall system size, the remainder of

this thesis will use the inductive flyback topology.

2.7 Relevant Measuring Techniques

The AC variation of CVAR constitutes an important parameter to characterize accu-

rately in the energy harvesting circuit. Such a circuit was proposed in [11] and willbe repeated here for convenience. Consider the op-amp network shown in Fig. 2-12.

There are two additional power line bypass capacitors not shown in the schematic;

one is a 0.22 MF film capacitor connected between v+ and ground while the other is

a 1 nF capacitor connected between v+ and v-.

If w

VR R

vssin(wt) C

Figure 2-13: Circuit to accurately determine the DC value of a capacitor.

which is valid under the assumption that CAC < CDC, it can be expressed as

VOUT =- -ivARR . (2.56)

Taking CvAR CDC + CAC sin (Lt),

VOUT = (10 V) wRCAC cos (wt) , (2.57)

which implies that

CAC = VOU . (2.58)A (10 V) wRHence, by measuring the output voltage at specific frequencies, CAC can be determined

as long as w < !. Note that purpose of C is to attenuate high frequency noise that

can severely mask the output signal.

The DC capacitance of CVAR also is a parameter of interest. Usually, this value

can be directly determined using a bridge circuit or a multimeter with capacitance

measuring capability. If an alternative method is desired, the circuit topology shown

in Fig. 2-13 can also be considered. This is nothing more than an impedance voltage

divider where1 (2.59)VC -1 + jwRCDcjV

with the hatted variables representing complex amplitudes. Taking the magnitudes

45

of both side,

Y C = vs (2.60)1 + (wRCDC)2

Finally, solving for CDC, one gets

CDC (i)2 (2.61)wR

As will be documented in Chapter 4, the circuits shown in Fig. 2-12 and Fig. 2-13

give CDC = 650 pF and CACMAX = 317.36 pF for the variable capacitor used in this

thesis.

2.8 Chapter Summary

This chapter mapped out the theoretical foundations behind energy harvesting cir-

cuits, the most important one being the Q-V plane contours and their relationshipto scavenged energy. Two typical capacitive conversion cycles were given - charge-

constrained and voltage-constrained - and the circuit topology explored in [11] wasgiven as an example employing charge-constrained cycles. However, due to the topol-

ogy's synchronous nature, excessive power consumption for the gate drive, and high

conduction loss, it is undesirable as an energy harvester. An alternative topology

based on an asynchronous diode charge pump connected to an energy flyback mech-

anism was proposed instead.

In order to sustain the efficiency of energy harvesting and to power the load

connected at the reservoir, three possible flyback circuits were analyzed, including the

inductor, direct shorting switch, and the capacitive bucket brigade. Although bulky,the inductive flyback allowed for maximum theoretical flyback efficiency, 100 %, and

required few components to implement. Hence, the topology chosen for this thesis

uses inductive flyback.

46

Comparing Eq. (2.15) and Eq. (2.34), it is apparent that parasitic diode capaci-tances hurt the overall conversion efficiency by decreasing the maximum voltage level

Cs can reach. This implies that diodes with low junction capacitance should beused for the charge pump. Furthermore, if the circuit is implemented on an IC, one

must observe careful circuit layout techniques to avoid creating excessive parasitic

capacitances.

The remaining chapters of this thesis builds upon the established foundations and

examine second-order effects that are difficult to characterize analytically. Chapter 3

examines in greater details the effect of device parasitics through the use of HSPICE,

a specialized circuit simulation program, and addresses energy flyback timing opti-

mization. Chapter 4 presents experimental results from a PCB that was designed

and optimized based on simulation results; the variable capacitor used will also be

characterized.

47

Chapter 3

Circuit Simulation and Design

Although the theoretical foundations of electric energy harvesting laid out in the pre-

ceding chapter are important, a computer-based simulation nonetheless is necessary

to pinpoint the most efficient circuit implementation. The discussion in Chapter 2

lacked specific component values, maximum tolerable parasitic sizes, and other im-

portant details necessary for the development of a successful prototype circuit board

(PCB). In this chapter, results from various HSPICE simulations that comprehen-sively survey the effect of different design choices will be first presented; they will

then lead to the formation of the actual circuit schematic upon which the final set of

experimental data presented in Chapter 4 is based.

3.1 Creating the Variable Capacitor

Because HSPICE inherently does not provide an easy way of simulating mechani-

cal variable capacitors with moving plates, the first task involves creating a circuit

equivalent that can represent the vibrating plates accurately enough. Based upon the

discussion in [14], a variable capacitor can be represented by a subcircuit consisting ofa fixed value capacitor in series with a dependent source whose voltage depends on the

48

iIN

CDC

ZIN - o VIN

AvIN

Figure 3-1: Subcircuit for simulating a variable capacitor.

voltage difference across the terminals of the subcircuit. Such a circuit configuration

is shown in Fig. 3-1. The two-port impedance of this subcircuit is

ZIN VIN _31IN SCDC(l+A)

Eq. (3.1) suggests that the subcircuit behaves equivalently to a capacitor that hascapacitance CDC (1 + A), which means that if A = sin (wt + #), the two-portmodel is precisely a variable capacitor with frequency W, DC value CDC, AC amplitude

CAC, and angle 4. Given the desired value for A, the dependent voltage source AVINmust have the value

CACAvIN = VIN 0 D sin (Wt + ~),(3.2)

which is simply a multiplication of the two-port voltage, a sinusoidal excitation of

amplitude 1, and a constant CAC/CDC.

Such a dependent voltage source can be specified in HSPICE through the use of a

polynomial function [15]; refer to Appendix (A) for the actual code implementing thevariable capacitor subcircuit. Verification of the variable capacitor implementation

involves attaching the subcircuit to a fixed voltage source Vs and gauging the amount

of current flowing into the subcircuit. Defining CvAR(t) = CDC + CAc(t), correctoperation requires

d dZIN -(VAR(S) = S- (AC(t)) -(3-3)

49

, eriod (sI Urrent(

0 5I L

)--5.26e-04 '-NI \I ~I ~I II II II I

I I I

II

1I MTime (tin) (TIME)

1.5m

Figure 3-2: Two-port input current of simulated variable capacitor forCAC = 300 pF, and Vs = 1 V. The vertical axis represents the inputin amps and the horizontal axis represents time plotted in seconds.

CDC = 1.22 nF,current plotted

As an example, if CDC = 1.22 nF, CAC = 300 sin (27r x 1900t) pF, and V = 1 V,the input current should be iIN = 3.58 cos (27r x 1900t) pA. Computer simulation ofthe two-port input current, shown in Fig. 3-2, confirms that the subcircuit behaves

correctly. Although shown with a sinusoidal variation, the capacitor model, through

additional parameter fitting, can also accommodate non-linear mechanical effects.

3.2 Inductor Modeling

A real wire-wound inductor will inevitably have parasitic losses associated with it.

Because the success of electric energy harvesting hinges upon high power conversion

efficiency, parasitic resistances associated with wire loss and core loss must be accu-

rately modeled. Capacitive effects, significant for radio frequency applications, will

not be considered here since environmental vibration doing work on the electrical

charges occur at much lower frequencies.

50

3.5u

3u

2.5u

2u

1 .5u

I U

500n

0

-500n

-1 U

-1.5u

-2u

-2.5u

-3u

-3.5u

2m

Rc

Rw L

Figure 3-3: Inductor modeled with core loss and winding loss.

Characterization of the energy flyback inductor has been performed in [11] usinga multimeter and a bridge instrument set at 300 kHz. The final model, with Rc

representing the core loss and Rw representing the winding loss, is shown in Fig. 3-

3. Extracted parameter values are L = 2.5 mH, chosen to limit the rate of current

ramping and prevent inductor saturation, RC = 360 kQ, and Rw = 8 Q for the exper-imental circuit. Note that by modeling the core loss as a linear resistor, one implicitly

disregards nonlinear loss mechanisms found in the inductor. Although not critical in

the simulation phase, these second-order effects turn out to be important when a

close fit between experimental data and simulation is desired. Refer to Chapter 4 for

more details.

3.3 Power Devices

Because the amount of energy harvested from the vibrational source is on the or-

der of several pW, power electronic components in the circuit, including diodes and

MOSFETs, also require accurate modeling to insure that the associated losses do not

exceed the converted energy. To model the components with precision, they must first

be selected. As with most circuits processing power, diodes exhibiting nearly ideal

behaviors are desirable; this translates to a low forward bias voltage drop, small par-

asitic resistance and capacitance, as well as low reverse bias leakage. Based on these

limitations, the 1N6263 Schottky barrier diode was selected. As will become evident

later from simulation results, the best MOSFET for energy harvesting should have

low on-resistance, small parasitic gate capacitance, and a weak body diode. These

51

requirements lead to the selection of a 2N7002 n-channel MOSFET for use in this

circuit.

Buermen extracted the appropriate HSPICE parameters for the 1N6263 Schottky

barrier diode in [161; Vishay, a company specializing in semiconductor devices, gen-erated the HSPICE model for the 2N7002 n-channel MOSFET. Briefly, the Schottky

barrier diode model contains two diodes, each with its own set of parameters, in par-

allel; one of them serves as a parasitic component. The n-channel MOSFET model

accounts for parasitic p-channel MOSFET, gate capacitance, and the body diode.

For the complete model files, refer to Appendix (A).

3.4 Oscilloscope Probes

As will be shown in simulations later during this chapter, the parasitic resistance

presented to the circuit due to the presence of oscilloscope probes can significantly

affect the energy conversion efficiency. In an extreme case, a simulation that results

in positive converted energy can see its reservoir voltage collapse when a 10 MQequivalent probe resistance is included as a load.

The significant problems posed by the scope probes arise because they form un-

expected current paths through which charge that had work done on it can leak to

ground, greatly decreasing conversion efficiency. As an example, if the scope probe

is attached to a point in the circuit with DC voltage VNODE = 2 V, the parasitic

resistance will on average dissipate

V2 22(PDIss) V R - 106 - 0.4 pW (3.4)

which could realistically exceed the amount of harvested energy.

In order to minimize probe loss, all probe points on the final PCB design require a

series 10 MQ resistor in front of the scope probe entry point; this halves the consumed

52

power at the expense of voltage resolution on the oscilloscope. With this in mind,

all simulations will have a 20 MQ parasitic resistance attached to probing nodes, themost prominent ones being VRES and vs, in order to assure that measurements can be

taken on the actual board.

3.5 Gate Drive Modeling

In order to feed the converted energy from the temporary storage capacitor Cs back

into the reservoir capacitor CRES, the n-channel MOSFET serving as a pass transistor

must be driven on and off in a timely fashion. The actual choice of drive strength and

frequency will be discussed later in the chapter after simulation results are presented,

but it is nonetheless important to discuss ways in which the clock signal can be

modeled with sufficient precision in HSPICE.

Based on the selection of an LMC555 CMOS timer configured in astable operation

as the gate drive, two important limitations must be modeled: finite rise time and

saturation voltage limits from Vss, the bottom power rail, and VDD, the top power

rail. These nonidealities are important because both contribute to additional power

loss during the conversion - finite rise time incur switching losses while saturation

voltage limits give rise to leakage current at the low end and higher than expected

channel on-resistance at the high end. From the LMC555 datasheet, the rise and fall

time are both 15 ns and the saturation voltage limit is 0.3 V from either supply rail.

3.6 Simulating the Two Diode Circuit

To better understand the energy harvesting process, the first part of the circuit,

namely the components of the charge pump, is simulated on its own. As a starting

point, a reservoir capacitor of value CRES = 1 MF and a storage capacitor of value

Cs =_ 3.3 nF are chosen; the value of Cs insures that parasitic capacitance from the

53

CRES VRES CVAR ~VAR CS VS

Figure 3-4: Charge pump portion of the energy harvester.

9.5 -A

9 -VS

-- 1, -8.5

vVAR i *

vRE

6.5

0 im 2m 3m 4m 5m 6m 7m 8mTime (1n) (TIME)

Figure 3-5: Voltage waveforms for energy harvesting circuit with CDC = 1.22 nF,CAC = 300 pF, CRES = 1 MF, Cs = 3.3 nF, and VINIT = 6 V. The vertical axisrepresents voltage plotted in volts and the horizontal axis represents time plotted inseconds.

oscilloscope probe and other sources do not dominate.

Fig. 3-4 shows the schematic for this section of the energy harvesting circuit,repeated from Chapter 2 for convenience. The schematic lacks any source of voltage

excitation; instead, before the simulation in HSPICE begins, all the individual node

voltages, VRES, VAR, and vs are initialized to 6 V. This allows the system to begin

with some initial energy that is necessary to start the energy conversion process. In

a real circuit, a battery that can be disconnected would serve as this initial energy

injection source.

54

During each cycle of operation, within which CRES decreases from its maximum

value and goes back up, energy flows from both the reservoir capacitor and the vi-

brational source into Cs, as shown earlier in Chapter 2. The voltage waveforms for

VRES, vAR, and vs plotted in Fig. 3-5 indicate the effects of these energy transfers. As

expected, the energy transferred to Cs causes vs to rise in accordance to Ws = 1Csvs.

At the same time, VRES drops as charge is pulled out of CRES and placed onto CVAR for

the vibrational source to do work on. However, because CRES > CVAR, the decrease

in VRES is insignificant, allowing VRES to be treated as a constant during this part

of the simulation. Furthermore, vVAR oscillates up and down as CVAR varies, also in

agreement with the predicted behavior.

In each energy conversion cycle,

WCONv =-Qovv (3.5)WCNV 2 QAVR=2 0(CMIN - CMAX) 35

where Qo is the amount of constrained charge and CMIN and CMAX are the minimumand maximum capacitance value for the vibrating capacitor. As more and more

conversion cycles occur, Qo decreases due to increasing difficulty of placing additionalcharge on CVAR (refer to Eq. (2.15)). This results in the decreasing step height forvs.

The theoretical maximum voltage that vs can obtain has been calculated in Chap-

ter 2. Using the derived formula,

VS,MAX - CMAX nSO= 1.65 x 6 V = 9.9 V (3.6)CMIN

if we take CDC = 1.22 nF and CAC = 300 sin (27r x 1900t) pF like in the earlierexample. Looking at Fig. 3-5, it is apparent that vs does not approach 9.9 V but

instead flattens out at around 9.5 V. This discrepancy stems from the fact that the

theoretical calculations presented in Chapter 2 ignored the forward bias voltage drop

of the Schottky barrier diodes.

55

20u

D116U ID216u -

6u -

0 1m 2m 3m 4m 5m 6m 7m 8mTime (11n) (TIME)

Figure 3-6: Current waveforms for charge pump circuit with CDC 1.22 nF, CAC =300 pF, CRES = 1 pF, Cs = 3.3 nF, and vINIT = 6 V. The vertical axis representscurrent plotted in amps and the horizontal axis represents time plotted in seconds.

Fig. 3-6 shows the current passing through the two diodes. The simulated wave-

forms shows that the diodes conduct in alternating fashion, in agreement with theory.

However, theoretical calculation ignored the effect of leakage current during the time

when diodes are reverse biased. Simulations later in this chapter confirms that diode

leakage has a detrimental effect on the efficiency of energy harvesting (due to thecareful selection of Schottky diodes with maximum Is = 0.15 pLA, the reverse bias

leakage current is not readily visible in the simulated waveforms).

Comparing the current and voltage waveforms, one finds that vs ramps up when

D 2 is conducting and stays flat when D1 is conducting. This makes sense intuitively

because the only time when harvested energy can flow into Cs occurs while D 2 con-

ducts. Finally, notice the decreasing amplitude of conducted current; this shows that

as vs rises, CvAR discharges less into Cs per cycle and therefore extracts fewer charges

from the reservoir.

For this part of the energy harvesting circuit to be considered successful, positive

56

net energy should result after a few cycles of vibrational motion. For any capacitor,

the change in stored energy given an original voltage vo and a final voltage vF is

A WC = C (v2 - v2) (3.7)

Using the same simulation parameters as above, the reservoir voltage droops from

VRES = 6 V to VRES = 5.9923 V after 4 cycles. During the same period of time, the

temporary storage node rises from vs = 6 V to vs = 8.2268 V. Therefore,

AWTOT = CRES (VRES,F - VRES,O) + (,F -~VS o) (3.8)

- 1 (10-" F) (0.092 V2) + 1 (3.3 x 10-9 F) (31.680 V2) (3.9)S6 nJ . (3.10)

The net energy of the system is rising, indicating a success in injecting mechanicalvibration energy into the circuit.

3.7 Two Diode Circuit with Energy Flyback

Now that the charge pump portion of the circuit has been shown to convert positive

energy, the inductive energy flyback consisting of a pass transistor, freewheeling diode,

and an inductor will be added. Their addition, along with a parasitic probe resistance

Rp mentioned earlier, completes the entire circuit except for the transistor gate drive;

the schematic is shown in Fig. 3-7.

As a first pass simulation, the gate of the MOSFET is driven in such